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Anton Baranov
Stability of the bases and frames reproducing kernels in model spaces
(Stabilité de bases et frames des noyaux reproduisants dans les espaces modèles)
Annales de l'institut Fourier, 55 no. 7 (2005), p. 2399-2422, doi: 10.5802/aif.2165
Article PDF | Reviews MR 2207388 | Zbl 1101.30036
Class. Math.: 46E22, 42C15, 30D55, 47B32
Keywords: Inner function, shift-coinvariant subspace, reproducing kernel, Riesz basis, frame, stability

Résumé - Abstract

We study the bases and frames of reproducing kernels in the model subspaces $K^2_{\Theta}=H^2\ominus \Theta H^2$ of the Hardy class $H2$ in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels $k_{\lambda_n}(z)= (1-\overline{\Theta(\lambda_n)}\Theta(z))/(z-\overline\lambda_n)$ under ``small'' perturbations of the points $\lambda_n$. We propose an approach to this problem based on the recently obtained estimates of derivatives in the spaces ${K^2_{\Theta}}$ and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.

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